# HISTORY OF MATHS PDF

The history of mathematics: an introduction / David M. Burton.—7th ed. p. cm. Includes bibliographical references and index. ISBN (alk. A Brief History of Mathematics. What is mathematics? What do mathematicians do? resourceone.info~rpyke/resourceone.info Cajori, F. The Teaching and History of Mathematics in the U. S.. Washington, 3. *Cantor, Moritz. Vorlesungen über Geschichte der Mathematik. Leipzig.

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There are many excellent reasons to study the history of mathematics. It helps We also encourage History of Mathematics courses taught to entering students. Euclid's Elements and its role in the history of Mathematics. 8. Archimedes, Eratosthenes. 9. Curves in the Greek Geometry, Apollonius the Great Geometer. own history of mathematics course to me; as one might expect, it was .. of science, and of the history of mathematics in particular. resourceone.info Fig.

As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. The Pythagoreans are credited with the first proof of the Pythagorean theorem , [38] though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.

Though he made no specific technical mathematical discoveries, Aristotle —c. The diagram accompanies Book II, Proposition 5. Although most of the contents of the Elements were already known, Euclid arranged them into a single, coherent logical framework. Euclid also wrote extensively on other subjects, such as conic sections , optics , spherical geometry , and mechanics, but only half of his writings survive.

Archimedes c. Apollonius of Perga c. AD 90— , a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years. Following a period of stagnation after Ptolemy, the period between and AD is sometimes referred to as the "Silver Age" of Greek mathematics. His main work was the Arithmetica, a collection of algebraic problems dealing with exact solutions to determinate and indeterminate equations.

He is known for his hexagon theorem and centroid theorem , as well as the Pappus configuration and Pappus graph. His Collection is a major source of knowledge on Greek mathematics as most of it has survived. The first woman mathematician recorded by history was Hypatia of Alexandria AD — He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements.

The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure.

Pythagoras held that at its deepest level, reality is mathematical in nature. Pythagoreans 11 represents a coherent body of mathematical doctrines believed that number rules the universe. They made no distinction between mathematics and physics and concern with the study of properties of counting numbers. They believe all measurements could be expressed in terms of natural numbers, or ratios of natural numbers.

They develop geometric theorems and insist that mathematical ideas required proofs. They think numbers had concrete representations as figures of point e. Posy12 points out three important Pythagorean beliefs: 1 they agree with Babylonian assumption of commensurability that any geometric measurement will be some rational multiple of the standard unit; 1 they think that space is ultimately discrete or separable that there is nothing between 1 and 2 and everything had to have atomic parts; and 3 they believe that continuity implied infinite divisibility.

J and Robertson, E.

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Its size is not known. You take 16 from 25 and there remains 9. What times what shall I take in order to get 9? Jones R. To say that the sum of two squares is equal to a third square meant that the two squares could be cut up and reassembled to form a square identical to the third square see Figure 2. Euclidean Geometry Around BC14, Euclid was studying geometry in Alexandria and wrote a thirteen-volume book that compiled all the known and accepted rules of geometry 15 called The Elements.

Euclid believes in absolute separation of discrete mathematics and magnitudes. Of the Element, for example, Books 5 and 6 state the theory of proportion for magnitudes, while Book 7 states the theory of proportion for numbers. In these Elements, Euclid attempted to define all geometrical terms 13 Berggren, J. Because mathematics is a science where every theorem is based on accepted assumptions, Euclid first had to establish some axioms with which to use as the basis of other theorems.

Euclid uses five axioms as the 5 assumptions, which he needs to prove all other geometric ideas. The use and assumption of these five axioms16 is what it called something to be categorized as Euclidean geometry. The first four postulates 18 state about straight line that may be drawn from any two points; any terminated straight line that may be extended indefinitely; a circle that may be drawn with any given center and any given radius; and all right angles that are congruent.

Explicitly, those postulates19 are as follows: Postulat I For every point P and for every point Q not equal to P there exists a unique line l that passes through P and Q. In the third postulate, Euclid had in mind drawing the circle with center A and radius r, and this postulate tell us that such a drawing is allowed Figure 3.

The fifth or the last postulate listed by Euclid stands out a little bit. It is a bit less intuitive and a lot more convoluted.

## History of mathematics

It looks like a condition of the geometry more than something fundamental about it. The fifth postulate is see Figure 4 : Postulate V If two straight lines lying in a plane are met by another line, and if the sum of he internal angles on one side is less than two right angles, then the straight lines will meet if the extended on the side on which the sum of the angles is less than two right angles.

From this postulate, we may have a question what is the criterion for line l to be parallel to line m? Non-Euclidean Geometry Pythagoras20 was the first who inclined to regard number theory as more basic than geometry.

The discovery of in-commensurable ratios presented them with a foundational crisis not fully resolved until the 19th century. Since Greek21, number theory, which concerns only whole numbers, cannot adequately deal with the magnitudes found in geometry.

Because of his belief that all things are numbers it would be a natural task to try to prove that the hypotenuse of an isosceles right angled triangle had a length corresponding to a number. For it found the irrational numbers, it can be proved that commensurability is false. To proof that commensurability is false we can use reductio ad absurdum procedure. Posy, C. This can not be proven from the other axioms.

See Figure 6 20 Jones, R.

He should have stated the "self-evident" assumptions. Modern mathematicians perceive that the Fifth Axiom of Geometry is too complex, and seemed derivable from the other postulates. Wallis, J. In other words, similarity preserves shape. Size, shape, and location are independent of each other and this simpler postulate allows derivation of Euclid's fifth postulate.

Meanwhile, Saccheri and Lambert 24 independently tried proving the parallel postulate by the reductio ad absurdum method. Their proof starts with "Neutral geometry" that is Euclidean geometry that excludes the parallel postulate.

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There 22 Posy, C. Saccheri and Lambert25 are repugnant to the nature of the straight line and space; and this was the discovery of non-Euclidean geometry.

In the late 18th and early 19th century, three men became interested in the acute angle hypothesis. Bolyai, Gauss, and Zobachevsky took the negation of the parallel postulate as a postulate and added it to neutral geometry; and resulting that nothing contradictory followed.

History of the theory of numbers Leonard Eugene Dickson Online Pages English The book 'History of the Theory of Numbers' presents the material related to the subjects of divisibility and primality.

History of Mathematics University of Oxford Online NA Pages English This course note is designed to provide the historical background to some of the mathematics familiar to students from A-level and the first four terms of undergraduate study, and looks at a period from approximately the mid-sixteenth century to the end of the nineteenth century. Free History Of Mathematics Books.

Abstract Algebra. Linear Algebra. Commutative Algebra. Complex Algebra. Elliptic Curves.

## A History of Mathematics

Geometric Algebra. Groups Theory. Higher Algebra.

Homological Algebra. Lie Algebra. Differential Algebra. Rings and Fileds.

Algebraic Geometry. Differential Geometry. Riemannian Geometry. Mathematical Analysis. Complex Analysis.Indians may well have learned of these decimal place value "rod numerals" from Chinese Buddhist pilgrims or other travelers, or they may have developed the concept independently from their earlier non-place-value system; no documentary evidence survives to confirm either conclusion. Rectangles do not exist. Homological Algebra.

Greeks came a proof of a general rule for finding all such sets of numbers called Pythagorean triples Figure. This book covers the period from antiquity to the close of World War I, with major emphasis on advanced mathematics and, in particular, the advanced mathematics of the nineteenth and early twentieth centuries. On the other hand, Leibniz's dy notation: , dy and dx are both very small that they are insignificant, however, dx their ratio is a number; thus ratios were stressed, not the individual components.

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